# Universal tests for memory words

G. Morvai, Benjamin Weiss

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

The main result is a universal pointwise test that, when presented with a set of words $S$ on a finite or countable alphabet ${\cal X}$ that purports to be a set of memory words for a stationary process, will eventually almost surely return the value YES precisely when all positive probability words in $S$ are memory words. For example, if $S$ consists of all of the single letters in ${\cal X}$, then the test will eventually say yes if and only if the process is a Markov chain. Various further positive and negative results of this type are also given.

Original language English 6532389 6873-6879 7 IEEE Transactions on Information Theory 59 10 https://doi.org/10.1109/TIT.2013.2268913 Published - 2013

### Fingerprint

Data storage equipment
Markov processes
Values

### Keywords

• stationary processes
• Statistical learning
• stochastic processes

### ASJC Scopus subject areas

• Information Systems
• Computer Science Applications
• Library and Information Sciences

### Cite this

Universal tests for memory words. / Morvai, G.; Weiss, Benjamin.

In: IEEE Transactions on Information Theory, Vol. 59, No. 10, 6532389, 2013, p. 6873-6879.

Research output: Contribution to journalArticle

Morvai, G. ; Weiss, Benjamin. / Universal tests for memory words. In: IEEE Transactions on Information Theory. 2013 ; Vol. 59, No. 10. pp. 6873-6879.
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